首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Approximating common fixed points of asymptotically nonexpansive mappings by composite algorithm in Banach spaces
Authors:Xiaolong Qin  Yongfu Su  Meijuan Shang
Institution:(1) Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300160, PR China;(2) Department of Mathematics, Shijiazhuang University, Shijiazhuang, 050035, PR China
Abstract:Let E be a uniformly convex Banach space and K a nonempty convex closed subset which is also a nonexpansive retract of E. Let T 1, T 2 and T 3: KE be asymptotically nonexpansive mappings with {k n }, {l n } and {j n }. 1, ∞) such that Σ n=1 (k n − 1) < ∞, Σ n=1 (l n − 1) < ∞ and Σ n=1 (j n − 1) < ∞, respectively and F nonempty, where F = {xK: T 1x = T 2x = T 3 x} = x} denotes the common fixed points set of T 1, T 2 and T 3. Let {α n }, {α′ n } and {α″ n } be real sequences in (0, 1) and ≤ {α n }, {α′ n }, {α″ n } ≤ 1 − for all nN and some > 0. Starting from arbitrary x 1K define the sequence {x n } by

$$\left\{ \begin{gathered}  z_n  = P(\alpha '_n T_3 (PT_3 )^{n - 1} x_n  + (1 - \alpha '_n )x_n ), \hfill \\  y_n  = P(\alpha '_n T_2 (PT_2 )^{n - 1} z_n  + (1 - \alpha '_n )x_n ), \hfill \\  x_{n + 1}  = P(\alpha _n T_1 (PT_1 )^{n - 1} y_n  + (1 - \alpha _n )x_n ). \hfill \\ \end{gathered}  \right.$$
(i) If the dual E* of E has the Kadec-Klee property then {x n } converges weakly to a common fixed point pF; (ii) If T satisfies condition (A′) then {x n } converges strongly to a common fixed point pF.
Keywords:Asymptotically nonexpansive  non-self map  Kadec-Klee property  Uniformly convex
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号